Unity Web Player should work in any browser that supports plugins (Internet Explorer, Safari, Firefox). Get more information about Unity's system requirements.

How can I test if Unity Web Player was installed correctly?

The Web Player download page (link above) detects and displays the version of Unity Web Player installed in your browser.

What if The Unity Web Player Install badge keeps showing up even after I installed the plugin?

Possible Solution Steps (Windows):

Uninstall the Unity Web Player (via Add/Remove Programs).

To be thorough, search for and delete all Unity temporary files.

Clear the browser cache.

Restart the computer.

Reinstall the Unity Web Player from https://unity3d.com/webplayer (as admin).

Notes:

Make sure to install the Unity Web Player as an admin. In managed environments, the average user sometimes doesn't have the permissions to install the plugin (which isn't always handled gracefully).

The installer exe file downloaded from unity3d.com/webplayer can also be used to install silently across multiple computers in a managed environment. For more information on how do do this, follow the link.